{
  "id": "1001.1081",
  "version": "v2",
  "published": "2010-01-07T14:47:01.000Z",
  "updated": "2010-06-07T16:33:57.000Z",
  "title": "Deformation of canonical morphisms and the moduli of surfaces of general type",
  "authors": [
    "F. J. Gallego",
    "M. González",
    "B. P. Purnaprajna"
  ],
  "comment": "32 pages. Final version with some simplifications and clarifications in the exposition. To appear in Invent. Math. (the final publication is available at springerlink.com)",
  "doi": "10.1007/s00222-010-0257-8",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this article we study the deformation of finite maps and show how to use this deformation theory to construct varieties with given invariants in a projective space. Among other things, we prove a criterion that determines when a finite map can be deformed to a one--to--one map. We use this criterion to construct new simple canonical surfaces with different $c_1^2$ and $\\chi$. Our general results enable us to describe some new components of the moduli of surfaces of general type. We also find infinitely many moduli spaces $\\mathcal M_{(x',0,y)}$ having one component whose general point corresponds to a canonically embedded surface and another component whose general point corresponds to a surface whose canonical map is a degree 2 morphism.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-07T16:33:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J29",
      "14J10",
      "14B10",
      "13D10"
    ],
    "keywords": [
      "general type",
      "canonical morphisms",
      "deformation",
      "general point corresponds",
      "finite map"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Inventiones Mathematicae",
      "year": 2010,
      "month": "Jun",
      "volume": 182,
      "number": 1,
      "pages": 1
    },
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010InMat.182....1G"
    }
  }
}